People at the hospital

Kaylina • Twin girls born 3/3
Ok ladies, I need to know if I'm being crazy on this one... Both my sister (who lives in Michigan and I love to death) and my sister in law (who lives an hour away and I'm not as close to) have asked if they can be at the hospital for the birth. I told my sister that a visit then probably wasn't a good idea, in part because I don't really want another visitor at that time (my mom will coming to live with us for a few months to help out as we're having twins).  And another part of me really doesn't want a bunch of people at the hospital. I'm thinking I just want it to be a time for my husband and I to bond with the babies.  Plus I'm not sure how I'll feel after the birth and really don't want to have to think about anyone beside me, my husband, and the babies. I could tell my sis was bummed.  
Then my sister in law is insisting we let her know when I go into labor so she can be at the hospital.  For all the same reasons I told her probably not. Her response was "well you can't stop me!" I was so mad that that's the approach she wanted to take instead of trying to understand why.  And in fact I can stop her by just not telling her.  But I know that's not the right approach either.
​I know they're just excited as neither of them have kids.  Is it wrong for me to want the birth to be more private? I really would just like to have visitors show up once we're ready and some of chaos has subsided. Is that selfish? Or should I still to my guns? 
​In addition, with twins, the babies will likely come early and there could be complications.  And I'm generally pretty introverted.  Would love your opinions!